IDNLearn.com provides a collaborative environment for finding and sharing knowledge. Our platform offers detailed and accurate responses from experts, helping you navigate any topic with confidence.

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Solve the equations for [tex]\( x \)[/tex] and match the solutions.

[tex]\[
\begin{array}{ll}
x=-\frac{3}{a} \quad x=\frac{6}{a} \quad x=-\frac{a}{6} \quad x=-\frac{6}{a} \quad x=\frac{3}{a} \\
x=\frac{a}{6} & x
\end{array}
\][/tex]

1. [tex]\(-ax - 20 = -14\)[/tex]
[tex]\(\square\)[/tex]

2. [tex]\(4 = \frac{6}{a} x + 5\)[/tex]
[tex]\(\square\)[/tex]

3. [tex]\(7 + 2ax = 13\)[/tex]
[tex]\(\square\)[/tex]


Sagot :

To solve each equation for [tex]\( x \)[/tex] and match the solutions:

1. Equation: [tex]\(-a x - 20 = -14\)[/tex]

- First, isolate [tex]\( -a x \)[/tex]:
[tex]\[ -a x - 20 + 20 = -14 + 20 \implies -a x = 6 \][/tex]
- Then, solve for [tex]\( x \)[/tex]:
[tex]\[ x = -\frac{6}{a} \][/tex]

Therefore, [tex]\(-a x - 20 = -14 \implies x = -\frac{6}{a}\)[/tex].

2. Equation: [tex]\(4 = \frac{6}{a} x + 5\)[/tex]

- First, isolate [tex]\(\frac{6}{a} x\)[/tex]:
[tex]\[ 4 - 5 = \frac{6}{a} x + 5 - 5 \implies -1 = \frac{6}{a} x \][/tex]
- Then, solve for [tex]\( x \)[/tex]:
[tex]\[ x = -\frac{a}{6} \][/tex]

Therefore, [tex]\(4 = \frac{6}{a} x + 5 \implies x = -\frac{a}{6}\)[/tex].

3. Equation: [tex]\(7 + 2 a x = 13\)[/tex]

- First, isolate [tex]\(2 a x\)[/tex]:
[tex]\[ 7 + 2 a x - 7 = 13 - 7 \implies 2 a x = 6 \][/tex]
- Then, solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{3}{a} \][/tex]

Therefore, [tex]\(7 + 2 a x = 13 \implies x = \frac{3}{a}\)[/tex].

Matching the solutions to each equation:

[tex]\[ \begin{array}{ll} -a x - 20 = -14 & \quad x = -\frac{6}{a} \\ 4 = \frac{6}{a} x + 5 & \quad x = -\frac{a}{6} \\ 7 + 2 a x = 13 & \quad x = \frac{3}{a} \end{array} \][/tex]
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.